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# THE RELATIONSHIP OF MUSICAL TONES.

## SCALES, AND TONALITY.

### Chapter XIII.

#### GENERAL VIEW OF THE DIFFERENT PRINCIPLES OF MUSICAL STYLE IN THE DEVELOPMENT OF MUSIC.

Up to this point our investigation has been purely physical. We have analysed the sensations of hearing, and investigated the physical and physiological causes for the phenomena discovered, — partial tones, combinational tones, and beats. In the whole of this research we have dealt solely with natural phenomena, which present themselves mechanically, without any choice, to all living beings whose ears are constructed on the same anatomical plan as our own. In such a field, where necessity is paramount and nothing is arbitrary, science is rightfully called upon to establish constant laws of phenomena, and to demonstrate strictly a strict connection between cause and effect. As there is nothing arbitrary in the phenomena embraced by the theory, so also nothing arbitrary can be admitted into the laws which regulate the phenomena, or into the explanations given for their occurrence. As long as anything arbitrary remains in these laws and explanations, it is the duty of science (a duty which it is generally able to discharge) to exclude it, by continuing the investigations.

But in this third part of our inquiry into the theory of music we have to furnish a satisfactory foundation for the elementary rules of musical composition, and here we tread on new ground, which is no longer subject to physical laws alone, although the knowledge which we have gained of the nature of hearing, will still find numerous applications. We pass on to a problem which by its very nature belongs to the domain of esthetics. When we spoke previously, in the theory of consonance, of agreeable and disagreeable, we referred solely to the immediate impression made on the senses when an isolated combination of sounds strikes the ear, and paid no attention at all to artistic contrasts and means of expression; we thought only of sensuous pleasure, not of esthetic beauty. The two must be kept strictly apart, although the first is an important means for attaining the second.

The altered nature of the matters now to be treated betrays itself by a purely external characteristic. At every step we encounter historical and national differences of taste. Whether one combination is rougher or smoother than another, depends solely on the anatomical structure of the ear, and has nothing to do with psychological motives. But what degree of roughness a hearer is inclined to endure as a means of musical expression depends on taste and habit; hence the boundary between consonances and dissonances has been frequently changed. Similarly Scales, Modes, and their Modulations have undergone multifarious alterations, not merely among uncultivated or savage people, but even in those periods of the world’s history and among those nations where the noblest flowers of human culture have expanded.

Hence it follows, — and the proposition is not even now sufficiently present to the minds of our musical theoreticians and historians — that the system of Scales, Modes, and Harmonic Tissues does not rest solely upon inalterable natural laws, but is also, at least partly, the result of esthetical principles, which have already changed, and will still further change, with the progressive development of humanity.

But it does not follow from this that the choice of those elements of musical art was perfectly arbitrary, and that they do not allow of being derived from some more general law. On the contrary the rules of any style of art form a well-connected system whenever that style has attained a full and perfect development. These rules of art were certainly never developed into a system by the artists themselves with conscious intention and consistency. They are rather the result of tentative exploration or the play of imagination, as the artists think out or execute their plans, and by trial gradually discover what kind or manner of performance best pleases them. Yet science can endeavour to discover the motors, whether psychological or technical, which have been at work in this artistic process. Scientific esthetics have to deal with the psychological motor; scientific physics with the technical. When the artist's aim in the style he has adopted, and its principal direction, have once been rightly conceived, it can be more or less correctly determined why he was forced to follow this or that rule, or employ this or that technical means. In musical theory, namely where the peculiar physiological functions of the ear, while not immediately present to conscious self-examination, play an important part, a large and rich field is thrown open for scientific investigation to shew the necessary character of the technical rules for each individual direction in the development of our art.

It does not rest with natural science to characterise the chief problem worked out by each school of art, and the elementary principle of its style. This must be gathered from the results of historical and esthetical inquiry.

The relation we have to treat may be illustrated by a comparison with architecture, which, like music, has pursued essentially different directions at different times. The Greeks, in their stone temples, imitated the original wooden constructions; that was the principle of their architectural style. The whole division and arrangement of their decorations clearly shew that it was their intention to imitate wooden constructions. The verticality of the supporting columns, the general horizontality of the supported beam, forced them to divide all the subordinate parts for the great majority of cases into vertical and horizontal lines. The purposes of Grecian worship, which performed its principal functions in the open air, were satisfied by erections, of this kind, in which the internal spaces were necessarily narrowly limited by the length of the stone or wooden beams which could be employed. The old Italians (Etruscans), on the other hand, discovered the principle of the arch, composed of wedge-shaped stones. This discovery rendered it possible to cover in much more extensive buildings with arched roofs, than the Greeks could do with their wooden beams. Among these arched buildings the halls of justice (basil'icae) became important, as is well known, for the subsequent development of architecture. The arched roof made the circular arch the chief principle in division and decoration for Roman (Byzantine) art. The columns, pressed by heavy weights, were transformed into pillars, on which, after the style was fully developed, columns merely appeared in diminished forms, half sunk in the mass of the pillar, as simply decorative articulations, and as the downward continuation of the ribs of the arches which radiated towards the ceiling from the upper end of the pillar.

In the arch the wedge-shaped stones press against each other, but as they all uniformly press inwards, each one prevents the other from falling. The most powerful and most dangerous degree of pressure is exerted by the stones in the horizontal parts of the arch, where they have either no support or no obliquely placed support, and are prevented from falling solely by the greater thickness of their upper extremities. In very large arches the horizontal middle portion is consequently the most dangerous, and would be precipitated by the slightest yielding of the materials. As, then, medieval ecclesiastical structures assumed continually larger dimensions, the idea occurred of leaving out the middle horizontal part of the arch altogether, and of making the sides ascend with moderate obliquity until they met in a pointed arch. From thenceforward the pointed arch became the dominant principle. The building was divided into sections externally by the projecting buttresses. These, and the omnipresent pointed arch, made the outlines hard, and the churches became enormously high. But both characters suited the vigorous minds of the northern nations, and perhaps the very hardness of the forms, thoroughly subdued by that marvellous consistency which runs through the varied magnificence of form in a gothic cathedral, served to heighten the impression of immensity and power.

We see here, then, how the technical discoveries which were associated with the problems as they rose successively created three entirely distinct principles of style — the horizontal line, the circular arch, the pointed arch — and how at each new change in the main plan of construction, all the subordinate individualities, down to the smallest decorations, were altered accordingly; and hence how the individual rules of construction can only be comprehended from the general principle of construction. Although the gothic style has developed the richest, the most consistent, the mightiest and most imposing of architectural forms, just as modern music among other musical styles, no one would certainly for a moment think of asserting that the pointed arch is nature’s original form of all architectural beauty, and must consequently be introduced everywhere. And at the present day it is well known that it is an artistic absurdity to put gothic windows in a Greek building. Conversely any one can unfortunately convince himself on visiting most of our gothic cathedrals how detestably unsuitable to the whole effect are those numerous little chapels of the renaissance period built in the Greek or Roman style. Just as little as the gothic pointed arch, should our diatonic major scale be regarded as a natural product. At least such an expression is quite inapplicable, except in so far as both are necessary and natural consequences of the principle of style selected. And just as little as we should use gothic ornamentation in a Greek temple, should we venture upon improving compositions written in ecclesiastical modes, by providing their notes with marks of sharps and flats in accordance with the scheme of our major and minor harmonies. The feeling for historical artistic conception has certainly made little progress as yet among our musicians, even among those who are at the same time musical historians. They judge old music by the rules of modern harmony, and are inclined to consider every deviation from it as mere unskilfulness in the old composer, or even as barbarous want of taste.[1]

Hence before we proceed to the construction of scales and rules for a tissue of harmony, we must endeavour to characterise the principles of style, at least for the chief phases of the development of musical art. For present purposes we may divide these into three principal periods : —

1. The Homophonic or Unison Music of the ancients, to which also belongs the existing music of Oriental and Asiatic nations.

2. The Polyphonic Music of the middle ages, with several parts, but without regard to any independent musical significance of the harmonies, extending from the tenth to the seventeenth century, when it passes into

3. Harmonic or Modern Music, characterised by the independent significance attributed to the harmonies as such. Its sources date back from the sixteenth century.

1. Homophonic Music.

One part music is the original form of music with all people. It still exists among the Chinese, Indians, Arabs, Turks, and modem Greeks, notwithstanding the greatly developed systems of music possessed by some of these nations.[2] That music in the time of highest Grecian culture, neglecting perhaps individual instrumental ornamentation, cadences, and interludes, was written in one part, or that the voices at most sang in Octaves, can now be considered as established. In the problems of Aristotle we find the question: 'Why is the consonance of the Octave alone sung? For this and no other consonance is played on the magădis'. This was a harp-shaped instrument [with a bridge dividing the strings at one-third their length]. In another place he remarks that the voices of boys and men form an Octave in singing.[3]

One part music, considered independently and unaccompanied by words, is too poor in forms and changes, to develop any of the greater and richer forms of art. Hence purely instrumental music at this stage is necessarily limited to short dances or marches. We really find no more among nations that have no harmonic music.[4] Performers on the flute[5] have certainly repeatedly gained the prize in the Pythian games, but it is possible to perform feats of execution in instrumental music in concise forms of composition, as, for example, in the variations of a short melody. That the principle of varying (μεταβολή) a melody with reference to dramatical expression (μίμησις), was known to the Greeks, follows also from Aristotle. He describes the matter very plainly, and remarks that choruses must simply repeat the melodies in the antistrophes, because it is easier for one than for several to introduce variations. But public competitors (ἀγωνισταί) and actors (ὑποκριταί) are able to grapple with these difficulties.[6]

Extensive works of art, in homophonic music, are only possible in connection with poetry, and this was also the way in which music was applied in classical antiquity. Not only were songs (odes) and religious hymns sung, but even tragedies and long epic poems were performed in some musical manner, and accompanied by the lyre. We are scarcely in a condition to form a conception of how this was done, because modern taste points in precisely the opposite direction, and demands from a great declaimer or public reader that he should produce a dramatic effect true to nature by the speaking voice alone, rating all approach to singing as one of the greatest of faults. Perhaps we have some echoes of the ancient spoken song in the singing tone of Italian declaimers, and the liturgical recitations (intoning) of the Roman Catholic priests. Indeed, attentive observation on ordinary conversation shews us that regular musical intervals involuntarily recur, although the singing tone of the voice is concealed under the noises which characterise the individual letters, and the pitch is not held firmly, but is frequently allowed to glide up and down. When simple sentences are spoken without being affected by feeling, a certain middle pitch is maintained, and it is only the emphatic words and the conclusions of sentences and clauses which are indicated by change of pitch.[7] The end of an affirmative sentence followed by a pause, is usually marked by the voice falling a Fourth from the middle pitch. An interrogative ending rises, often as much as a Fifth above the middle pitch. For example a bass voice would say:

Emphasised words are also rendered prominent by their being spoken about a Tone higher than the rest,[8] and so on. In solemn declamation the alterations of pitch are more numerous and complicated. Modern recitative has arisen from attempting to imitate these alterations of pitch by musical notes. Its inventor, Giacomo Peri, in the preface to his opera of Eurydice, published in 1600, distinctly says as much. An attempt was then made to restore the declamation of ancient tragedies by means of recitative. Ancient recitative certainly differed somewhat from modern recitative, by preserving the metre of the poems more exactly, and by having no accompanying harmonies. Nevertheless our recitative, when well performed, will give us a better conception of the degree in which the expression of the words can be enhanced by musical recitation, than we can obtain from the monotonous repetition of the Roman liturgy, although the latter perhaps is more nearly related in kind to ancient recitation than the former. The settlement of the Roman liturgy by Pope Gregory the Great (A.D. 590 to 604) reaches back to a time in which reminiscences of the ancient art, although faded and deformed, might have been in some degree handed down by tradition, especially if, as we are probably entitled to assume, Gregory really did little more than finally establish the Roman school of singing which had existed from the time of Pope Sylvester (A.D. 314 to 335).[9] The majority of these formulae for lessons, collects, &c., evidently imitate the cadence of ordinary speech. They proceed at an equal height; particular, emphatic, or non-Latin words are somewhat altered in pitch; and for the punctuation certain concluding forms are prescribed, as the following for lessons, according to the customs of Münster.[10]

These and similar final formulae were varied according to the solemnity of the feast, the subject treated, the rank of the priest that sang and that answered, and so on.[10] It is easy to see that they strove to imitate the natural cadences of ordinary speech, and to give them solemnity by eliminating their individual irregularities. Of course in such fixed formula no regard can be paid to the grammatical sense of the clauses, which suffers much in various ways from the intoning. Similarly we may suppose that the ancient tragic poets prescribed the cadences of speech to their actors, and preserved them by a musical accompaniment. And since ancient tragedy kept much further aloof from immediate external realism than our modern drama, as is shewn by the artificial rhythms, the unusual rolling words, the immovable strange masks, it could admit of a more singing tone for declamation than would, perhaps, please our modern ears. Then we must remember that by emphasising or increasing the loudness of certain words, and by rapidity or slowness of speech, or pantomimic action, much life can be thrown into delivery of this kind, which would certainly be insufferably monotonous if not thus enlivened.

But in any case homophonic music, even when in olden time it had to accompany extensive poems of the highest character, necessarily played an utterly subordinate part. The musical turns must have entirely depended on the changing sense of the words, and could have had no independent artistic value or connection without them. A peculiar melody for singing hexameters throughout an epic, or iambic trimeters throughout a tragedy, would have been insupportable.[11]Those melodies (νόμοι) which were allotted to odes and tragic choruses, were certainly freer and more independent. For odes there were also well-known melodies (the names of some of them are preserved) to which fresh poems were continually composed.

In the great artistic works just mentioned, then, music must have been entirely subordinate; independently, it could only have formed short pieces. Now this is closely connected with the development of homophonic music as a musical system. Among the nations who possess such music we always find certain degrees of pitch selected for the melodies to move in. These scales are very various in kind, partly, it would seem, very arbitrary, so that many appear to us quite strange and incomprehensible, and yet the best gifted among those nations which possess them, as the Greeks, Arabs, and Indians, have developed them in an extremely subtile and varied manner. [See App. XX. sect. K.]

When speaking of these systems of tones, it becomes a question of essential importance for our present purpose, to inquire whether they are based upon any determinate reference of all the tones in the scale to one single principal and fundamental tone, the tonic or key-note. Modern music effects a purely musical internal connection among all the tones in a composition, by making their relationship to one tone as perceptible as possible to the ear. This predominance of the tonic, as the link which connects all the tones of a piece, we may, with Fétis, term the principle of tonality. This learned musician has properly drawn attention to the fact that tonality is developed in very different degrees and manners in the melodies of different nations. Thus in the songs of the modern Greeks, and chants of the Greek Church, and the Gregorian tones of the Roman Church, they are not developed in a manner which is easy to harmonise, whereas, according to Fétis,[12] it is on the whole easy to add accompanying harmonies to the old melodies of the northern nations of German, Celtic, and Sclavonic origin.

It is indeed remarkable that though the musical writings of the Greeks often treat subtile points at great length, and give the most exact information about all other peculiarities of the scale, they say nothing intelligible about a relation which in our modern system stands first of all, and always makes itself most distinctly sensible. The only hints to be found concerning the existence of the tonic are not in especial musical writings, but as before in the works of Aristotle, who asks : —

'Why is it that if any one alters the tone on the middle string (μέση) after the others have been tuned, and plays, every thing sounds amiss, not merely when he comes to this middle tone, but throughout the whole melody? but if he alters the tone played by the forefinger [13] or any other, the difference is only perceived when that string is struck? Is there a good reason for this? All good melodies often employ the tone of the middle string, and good composers often come upon it, and if they leave it recur to it again; but this is not the case with any other tone.' Then he compares the tone of the middle string with conjunctions in language, such as ‘ and ’ [and ‘ then ’], without which language could not exist, and proceeds to say : 'In this way the tone of the middle string is a link between tones, especially of the best tones, because its tone most frequently recurs'.[14] And in another place we find the same question with a slightly different answer, 'Why do the other tones sound badly when the tone of the middle string is altered? but if the tone of the middle string remains, and one of the others is altered, the altered one alone is spoiled? Is it because that all are tuned and have a certain relation to the tone of the middle string, and the order of each is determined by that? The reason of the tuning and connection being removed, then, things no longer appear the same.'[15] In these sentences the esthetic significance of the tonic, under the name of 'the tone of the middle string,' is very accurately described. To this we may add that the Pythagoreans compared the tone of the middle string with the sun, and the other tones in the scale with the planets.[16] It appears as if it had been usual to begin with the tone of the middle string above mentioned, for we read in the 33rd problem of Aristotle: 'Why is it more agreeable to proceed from high pitch to low pitch, than from low pitch to high pitch? Can it be that we thus begin at the beginning? for the tone of the middle string is also the leader of the tetrachord and highest in pitch. The second way would be to begin at the end instead of at the beginning. Or can it be that tones of lower pitch sound nobler and more euphonious after tones of high pitch?[17] This seems also to shew that it was not the custom to end with the tone of the middle string, which commenced, but with the tone of lowest pitch [produced by the uppermost string or Hypatē], of which last tone Aristotle, in his 4th problem, says that, as opposed to its neighbour, the tone of lowest pitch but one, [due to the string of highest position but one, or Parhypatē,] it is sung with complete relaxation of all the effort that is felt in the other. [18] These words of Aristotle may certainly be applied to the national Doric scale of the Greeks, which, increased by Pythagoras to eight tones, was as follows : —

$$\mathrm{Tetrachord \enspace of \enspace lowest \enspace pitch = \begin{cases} \mathrm{E \quad Hypătē \quad [ὑπάτη \quad uppermost \enspace string]} \\ \mathrm{F \quad Parhypătē \quad [παρυπάτη \quad next \enspace to \enspace uppermost \enspace string]} \\ \mathrm{G \quad Lichănos \quad [λίϰανοϛ \quad forefinger \enspace string]} \\ \mathrm{A \quad Mĕsē (tone \enspace of \enspace middle \enspace string) \quad [μέση \quad middle \enspace string]} \end{cases} }$$ $$\mathrm{Tetrachord \enspace of \enspace highest \enspace pitch} = \begin{cases} \mathrm{B \quad Paramĕsē \quad [παραμέση \quad next \enspace to \enspace middle \enspace string]} \\ \mathrm{C \quad trĭte \quad [τρίτη \quad third \enspace string]} \\ \mathrm{D \quad Paranētē \quad [παρανήτη \quad next \enspace to \enspace lowermost \enspace string]} \\ \mathrm{E \quad Nētē \quad [νήτη \quad lowermost \enspace string]} \end{cases}$$

In modern phraseology the last description cited from Aristotle implies that the Parhypatē was a kind of descending 'leading note' to the Hypatē. In the leading tone there is perceptible effort, which ceases on its falling into the fundamental tone.

If, then, the tone of the middle string answers to the tonic, the Hypatē, which is its Fifth, will answer to the dominant. For our modern feeling it is far more necessary to close with the tonic than to begin with it, and hence we usually take the final tone of a piece to be its tonic without further inquiry. Modern music, however, usually introduces the tonic also in the first beat of the opening bar. The whole mass of tone is developed from the tonic and returns into it. Modern musicians cannot obtain complete repose at the end unless the series of tones converges into its connecting centre.

Ancient Greek music seems, then, to have deviated from ours by ending on the dominant instead of the tonic. And this is in full agreement with the intonation of speech. We have seen that the end of an affirmative sentence is likewise formed on the Fifth next below the principal tone.[19] This peculiarity has also been generally preserved in modem recitative, in which the singer usually ends on the dominant; the accompanying instruments then make this tone part of the chord of the dominant Seventh, leading to the tonic chord, and thus make a close on the tonic in accordance with our present musical feeling. Now since Greek music was cultivated by the recitation of epic hexameters and iambic trimeters, we should not be surprised if the above-mentioned peculiarities of chanting were so predominant in the melodies of odes that Aristotle could regard them as the rule.[20]

From the facts just adduced it follows (and this is what we are chiefly concerned with) that the Greeks, among whom our diatonic scale first arose, were not without a certain esthetic feeling for tonality, but that they had not developed it so decisively as in modem music. Indeed, it does not appear to have even entered into the technical rules for constructing melodies. Hence Aristotle, who treated music esthetically, is the only known writer who mentions it; musical writers proper do not speak of it at all. And unfortunately the indications furnished by Aristotle are so meagre, that doubt enough still exists. For example, he says nothing about the differences of the various musical modes in reference to their principal tone, so that the most important point of all from which we should wish to regard the construction of the musical scale, is almost entirely obscured.

The reference to a tonic is more distinctly made out in the scales of the old Christian ecclesiastical music. Originally the four so-called authentic scales were distinguished, as they had been laid down by Ambrose of Milan (elected Bishop A.D. 374, died A.D. 398). Not one of these agrees with any one of our scales. The four plagal scales afterwards added by Gregory, are no scales at all in our sense of the word. The four authentic scales of Ambrose[21] are:

 1) $$D$$ $$E$$ $$F$$ $$G$$ $$A$$ $$B$$ $$c$$ $$d$$ 2) $$E$$ $$F$$ $$G$$ $$A$$ $$B$$ $$c$$ $$d$$ $$e$$ 3) $$F$$ $$G$$ $$A$$ $$B$$ $$c$$ $$d$$ $$e$$ $$f$$ 4) $$G$$ $$A$$ $$B$$ $$c$$ $$d$$ $$e$$ $$f$$ $$g$$

Perhaps, however, the change of $$B$$ into $$B\flat$$ was allowed from the first, and this would make the first scale agree with our descending scale of $$D$$ minor, and the third scale would become our scale of $$F$$ major. The old rule was that songs in the first scale should end in $$D$$, those in the second in $$E$$, those in the third in $$F$$, and those in the fourth in $$G$$. This marked out these tones as tonics in our sense of the word. But the rule was not strictly observed. The conclusion might fall on other tones of the scale, the so-called confinal tones, and at last the confusion became so great that no one was able to say exactly how the scale was to be recognised, all kinds of insufficient rules were formulated, and at last musicians clung to the mechanical expedient of fixing upon certain initial and concluding phrases, called tropes, as characterising the scale.

Hence although the rule of tonality had been already remarked in these medieval ecclesiastical scales, the rule was so unsettled and admitted so many exceptions, that the feeling of tonality must have been much less developed than in modern music.

The Indians also hit upon the conception of a tonic, although their music is likewise unisonal. They called the tonic Ansa.[22] Indian melodies as transcribed by English travellers, seem to be very like modern European melodies.[23] Fétis and Coussemaker[24] have made the same remark respecting the few known remains of old German and Celtic melodies.

Although, therefore, homophonic music was [possibly] not entirely without a reference to some tonic, or predominant tone, such a tone was beyond all dispute much more weakly developed than in modern music, where a few consecutive chords suffice to establish the scale in which that portion of the piece is written. The cause of this seems to me traceable to the undeveloped condition and subordinate part which characterises homophonic music. Melodies which move up and down in a few tones which are easily comprehended, and are connected, not by some musical contrivance, but by the words of a poem, do not require the consistent application of any contrivance, to combine them. Even in modern recitative tonality is much less firmly established than in other forms of composition. The necessity for a steady connection of masses of tone by purely musical relations, does not dawn distinctly on our feeling, until we have to form into one artistic whole large masses of tone, which have their own independent significance without the cement of poetry.

2. Polyphonic Music.

The second stage of musical development is the polyphonic music of the middle ages. It is usual to cite as the first invented part-music, the so-called organum or diaphony, as originally described by the Flemish monk Hucbald at the beginning of the tenth century. In this, two voices are said to have proceeded in Fifths or Fourths, with occasional doublings of one or both in Octaves. This would produce intolerable music for modern ears. But according to O. Paul[25] the meaning is not that the two voices sang at the same time, but that there was a responsive repetition of a melody in a transposed condition, in which case Hucbald would have been the inventor of a principle which subsequently became so important in the fugue and sonata.

The first undoubted form of part-music intentionally for several voices, was the so-called discantus, which became known at the end of the eleventh century in France and Flanders. The oldest specimens of this kind of music which have been preserved are of the following description. Two entirely different melodies — and to all appearance the more different the better — were adapted to one another by slight changes in rhythm or pitch, until they formed a tolerably consonant whole. At first, indeed, there seems to have been an inclination for coupling a liturgical formula with a rather 'slippery' song. The first of such examples could scarcely have been intended for more than musical tricks to amuse social meetings. It was a new and amusing discovery that two totally independent melodies might be sung together and yet sound well.

The principle of discant was fertile, and its nature was suitable for development at that period. Polyphonic music proper was its issue. Different voices, each proceeding independently and singing its own melody, had to be united in such a way as to produce either no dissonances, or merely transient ones which were readily resolved. Consonance was not the object in view, but its opposite, dissonance, was to be avoided. All interest was concentrated on the motion of the voices. To keep the various parts together, time had to be strictly observed, and hence the influence of discant developed a system of musical rhythm, which again contributed to infuse greater power and importance into melodic progression. There was no division of time in the Gregorian Cantus firmus. The rhythm of dance music was probably extremely simple. Moreover, melodic movement increased in richness and interest as the parts were multiplied. But the establishment of an artistic connection between the different voices, which, as we have seen, were at first perfectly free, required a new invention, and this, though it cropped up at first in a very humble form, has ended by obtaining predominant importance in the whole art of modern musical composition. This invention consisted in causing a musical phrase which had been sung by one voice to be repeated by another. Thus arose canonic imitation, which may be met with sporadically as early as in the twelfth century.[26] This subsequently developed into a highly artistic system, especially among Netherland composers, who, it must be owned, ended by often shewing more calculation than taste in their compositions.

To this condition of the art corresponded the condition of the tonal system. The old ecclesiastical scales were retained in their essentials, the first from $$D$$ to $$d$$, the second from $$E$$ to $$e$$, the third from $$F$$ to $$f$$, and the fourth from $$G$$ to $$g$$. Of these the scale from $$F$$ to $$f$$ was useless for harmonic purposes, because it contained the Tritone $$F - B$$, in place of the Fourth $$F - B\flat$$. Again, there was no reason for excluding the scales from $$C$$ to $$c$$ and $$A$$ to $$a$$. And thus the ecclesiastical scales altered under the influence of polyphonic music. But as the old unsuitable names were retained notwithstanding the changes, there arose a terrible confusion in the meaning attached to modes. It was not till nearly the end of this period that a learned theoretician, Glarean, undertook in his Dodecachordon (Basle 1547) to put some order into the theory of modes. He distinguished twelve of them, six authentic and six plagal, and assigned them Greek names, which were, however, incorrectly transferred. However, his nomenclature for ecclesiastical modes has been generally followed ever since. The following are Glarean’s six authentic ecclesiastical modes, keys or scales, with the incorrect Greek names he assigned to them.

 Ionic $$C$$ $$D$$ $$E$$ $$F$$ $$G$$ $$A$$ $$B$$ $$c$$ Doric $$D$$ $$E$$ $$F$$ $$G$$ $$A$$ $$B$$ $$c$$ $$d$$ Phrygian $$E$$ $$F$$ $$G$$ $$A$$ $$B$$ $$c$$ $$d$$ $$e$$ Lydian $$F$$ $$G$$ $$A$$ $$B$$ $$c$$ $$d$$ $$e$$ $$f$$ Mixolydian $$G$$ $$A$$ $$B$$ $$c$$ $$d$$ $$e$$ $$f$$ $$g$$ Eolic $$A$$ $$B$$ $$c$$ $$d$$ $$e$$ $$f$$ $$g$$ $$a$$

Ionic answers to our major, Eolic to our minor system. Lydian was scarcely ever used in polyphonic music owing to the false Fourth $$F - B$$, and when it was employed it was altered in many different ways.

Inability to judge of the musical significance of a connected tissue of harmonies again appears in the theory of the keys, by the rule, that the key of a polyphonic composition was determined by considering the separate voices independently. Glarean in certain compositions attributes different keys to the tenor and bass, the soprano and alto. Zarlino assumes the tenor as the chief part for determining the key.

The practical consequences of this neglect of harmony are conspicuous in various ways in musical compositions. The composers confined themselves on the whole to the diatonic scale; 'accidentals,' or signs of alterations of tone, were seldom used. The Greeks had introduced the depression of the tone $$B$$ to $$B\flat$$ in a peculiar tetrachord, that of the synēmmenoi, and this was retained. Besides this $$f\sharp$$, $$c\sharp$$, and $$g\sharp$$ were used, to introduce leading tones in the cadences. Hence modulation, as we understand it, from the key of one tonic to that of another with a different signature was almost entirely absent. Moreover, the chords used by preference down to the end of the fifteenth century, were formed of the Octave and Fifth without the Third, and such chords now sound poor and are avoided as much as possible. To medieval composers who only felt the want of the most perfect consonances, these chords appeared the most agreeable, and none others might be used at the close of a piece. The dissonances which occur are universally those which arise from suspended and passing tones; chords of the dominant Seventh, which, in modern harmony, play such an important part in marking the key, and in connecting and facilitating progressions, were quite unknown.

Great, then, as was the artistic advance in rhythm and the progression of parts, during this period, it did little more for harmony and the tonal system than to accumulate an undigested mass of experiments. Since the involved progression of the parts gave rise to chords in extremely varied transpositions and sequences, the musicians of this period could not but hear these chords and become acquainted with their effects, however little skill they shewed in making use of them. At any rate, the experience of this period prepared the way for harmonic music proper, and made it possible for musicians to produce it, when external circumstances forced on the discovery.

3. Harmonic Music.

Modern harmonic music is characterised by the independent significance of its harmonies, for the expression and the artistic connection of a musical composition. The external inducements for this transformation of music were of various kinds. First there was the Protestant ecclesiastical chorus. It was a principle of Protestantism that the congregation itself should undertake the singing. But a congregation could not be expected to execute the artistic rhythmical labyrinths of Netherland polyphony. On the other hand, the founders of the new confession, with Luther at their head, were far too penetrated with the power and significance of music, to reduce it at once to an unadorned unison. Hence the composers of Protestant ecclesiastical music had to solve the problem of producing simply harmonised chorales, in which all the voices progressed at the same time. This excluded those canonic repetitions of the same melodic phrases in different parts, which had hitherto formed the chief unity of the whole piece. A new connecting principle had to be looked for in the sound of the tones themselves, and this was found in a stricter reference of all to one predominant tonic. The success of this problem was facilitated by the fact that the Protestant hymns were chiefly adapted to existing popular melodies, and the popular songs of the Germanic and Celtic races, as already remarked, betrayed a stricter feeling for tonality in the modern sense, than those of southern nations. Thus as early as in the sixteenth century, the system of the harmony of the ecclesiastical Ionic mode (our present major) developed itself with tolerable correctness, so that these chorales do not strike modern ears as strange, although they were still without many of our later contrivances for marking the key, as, for example, the chord of the dominant Seventh. On the other hand, it was much longer before the other ecclesiastical modes, in harmonising which much uncertainty still prevailed, were fused into the modern minor mode. The Protestant ecclesiastical hymns of that time produced great effects on the feelings of contemporaries — a fact emphasised on all sides in the liveliest language, so that no doubt can exist that the impression made by such music, was something as new as it was peculiarly powerful.

In the Roman Church also a desire arose for altering their music. The divisions of polyphonic music scattered the sense of the words, and made them unintelligible to the unpractised public, and occasioned even a learned and cultivated hearer great difficulties in endeavouring to disentangle the knot of voices. In consequence of the proceedings of the Council of Trent, and by an order of Pope Pius IV. (A.D. 1559-1565), Palestrina (A.D. 1524-1594) carried out this simplification and embellishment of ecclesiastical music, and the simple beauty of his compositions is said to have prevented the complete banishment of part music from the Roman liturgy. Palestrina, who wrote for choruses of singers practised in their art, did not entirely drop the more complicated progression of parts found in polyphonic music, but by appropriate sections and divisions he separated and connected both the mass of tones and the mass of voices, and generally distributed the latter into several distinct choirs. The voices also are more or less frequently heard together in such progressions as were used in chorales, and in this case consonant chords greatly predominated. By this means he made his pieces more comprehensible and intelligible, and in general extremely agreeable to the ear. But the deviation of ecclesiastical modes from the new modes invented in modern times for the treatment of harmonies, is nowhere so remarkable as in the compositions of Palestrina, and those of contemporary Italian composers of ecclesiastical music, among whom Giovanni Gabrieli, a Venetian, should be particularly named. Palestrina was a pupil of Claude Goudimel (a Huguenot, slain at Lyons in the massacre of St. Bartholomew), who had harmonised French psalms in a way which, when the scale was major, was but very slightly different from modern habits. These psalm melodies had been borrowed, or at least imitated from popular songs. Hence Palestrina was certainly acquainted with this mode of treatment, through his teacher, but he had to deal with themes from the Gregorian Cantus firmus that moved in ecclesiastical tones, which he was forced to maintain strictly even in pieces where he himself invented or adapted the melodies. Now these modes necessitated a totally different harmonic treatment, which sounds very strange to moderns. As a specimen I will only cite the commencement of his eight-part Stabat mater.

Here, at the commencement of a piece, just where we should require a steady characterisation of the key, we find a series of chords in the most varied keys, from $$A$$ major to $$F$$ major, apparently thrown together at haphazard, contrary to all our rules of modulation. What person that was ignorant of ecclesiastical modes could guess the tonic of the piece from this commencement? As such we find $$D$$ at the end of the first strophe, and the sharpening of $$C$$ to $$C\sharp$$ in the first chord also points to $$D$$. The principal melody too, which is given to the tenor, shews from the commencement that $$D$$ is the tonic. But we do not get a minor chord of $$D$$ till the eighth bar, whereas a modern composer would have been forced to introduce it in the first good place he could find in the first bar.

We see from these characters how greatly the nature of the whole system of ecclesiastical modes differed from our modern keys. We cannot but assume that masters like Palestrina founded their method of harmonisation upon a correct feeling for the peculiar character of those modes, and that, as they could not fail to be acquainted with the contemporary advances in Protestant ecclesiastical music, their work was neither arbitrary nor unskilful.

What we miss in such examples as the one just adduced, is first, that the tonic chord does not play the same prominent part at the very commencement that is assigned to it in modern music. In the latter, the tonic chord has the same prominent and connecting significance among chords as the tonic or key-note among the tones of the scale. Next we miss altogether that feeling for the connection of consecutive chords which in modern times has led to the very general custom of giving them a common tone. This is evidently related to the fact that, as we shall see hereafter, it was not possible in the old ecclesiastical modes to produce chains of chords so closely connected with each other and with the tonic chord, as in the modern major and minor modes.

Hence, although we recognise in Palestrina and Gabrieli a delicate artistic sensitiveness for the esthetic effect of separate chords of various kinds, and in so far a certain independent significance in their harmonies, yet we see that the means of establishing an internal connection in the tissue of chords had still to be discovered. This problem, however, required a reduction and transformation of the previous scales, to our major and minor. On the other hand, this reduction sacrificed the great variety of expression which depended on diversity of scale. The old scales partly form transitions between major and minor, and partly enhance the character of the minor, as in the ecclesiastical Phrygian mode [p. 245], This diversity being lost, it had to be replaced by new contrivances, such as the transposition of the scales for different tonics, and the modulational passage from one key to another.

This transformation was completed during the seventeenth century. But the most active cause for the development of harmonic music is due to the commencement of opera. This had been occasioned by a revival of acquaintance with classical antiquity, and its avowed object was to rehabilitate ancient tragedy, which was known to have been recited musically. Here arose immediately the problem of allowing one or two voices to execute solos; but these again had to be harmonised so as to fit in between the choruses, which were treated in the polyphonic manner, the object being to make the solo parts stand prominently forward and keep the accompanying voices well under. These conditions first gave rise to Recitative, invented by Giacomo Peri and Caccini in 1600, and solo songs with airs, invented by Claudio Monteverde and Viadana. The new view taken of harmony shews itself in written music by the appearance of figured basses in the works of these composers. Every figured bass note represented a chord, so that the chords themselves were settled, but the progression of the parts of which they were constituted was left to the taste of the player. And thus what was merely secondary in polyphonic music, became principal, and conversely.

Opera also necessitated the discovery of more powerful means of expression than were admissible in ecclesiastical music. Monteverde, who was extremely prolific in inventions, is the first composer who used chords of the dominant Seventh without preparation, for which he was severely blamed by his contemporary Artusi. Generally we find a bolder use of dissonances, which were employed independently, to express sharp contrasts of expression, and not, as before, as accidental results of the progression of parts.

Under these influences, even as early as in Monteverde’s time, the Doric, Eolic, and Phrygian ecclesiastical modes [p. 254] began to be transformed and fused into our modern minor mode. This was completed in the seventeenth century, and these modes were thus made more suitable for giving prominence to the tonic of the harmony, as will be more fully shewn hereafter.

We have already given an outline of the nature of the influence which these changes exerted on the constitution of the tonal system. The mode of connecting musical phrases hitherto in vogue — canonic repetitions of similar melodic figures — had necessarily to be abandoned as soon as a simple harmonic accompaniment had to be subordinated to a melody. Hence some new means of artistic connection had to be discovered in the sound of the chords themselves. This was effected, first by making the harmonies refer their tones much more definitely to one predominant tonic than before, and secondly by giving fresh strength to the relations between the chords themselves and between all other chords and the tonic chord. In the course of our investigations we shall see that the distinctive peculiarities of the modern system of tones can be deduced from this principle, and that the principle itself is very strictly carried out in our present music. In reality the mode in which the materials of music are now worked up for artistic use, is in itself a wondrous work of art, at which the experience, ingenuity, and esthetic feeling of European nations has laboured for between two and three thousand years, since the days of Terpander and Pythagoras. But the complete formation of the essential features as we now see it, is scarcely two hundred years old in the practice of musical composers, and theoretical expression was not given to the new principle till the time of Rameau at the beginning of last century. In the historical point of view, therefore, it is wholly the product of modern times, limited nationally to the German, Roman, Celtic, and Sclavonic races.

With this tonal system, which admits great wealth of form with strictly defined artistic consistency, it has become possible to construct works of art, of much greater extent, and much richer in forms and parts, much more energetic in expression, than any producible in past ages; and hence we are by no means inclined to quarrel with modern musicians for esteeming it the best of all, and devoting their attention to it exclusively. But scientifically, when we proceed to explain its construction and display its consistency we must not forget that our modern system was not developed from a natural necessity, but from a freely chosen principle of style; that beside it, and before it, other tonal systems have been developed from other principles, and that in each such system the highest pitch of artistic beauty has been reached, by the successful solution of more limited problems.

This reference to the history of music was necessitated by our inability in this case to appeal to observation and experiment for establishing our explanations, because, educated in a modern system of music, we cannot thoroughly throw ourselves back into the condition of our ancestors, who knew nothing about what we have been familiar with from childhood, and who had to find it all out for themselves. The only observations and experiments, therefore, to which we can appeal, are those which mankind themselves have undertaken in the development of music. If our theory of the modern tonal system is correct it must also suffice to furnish the requisite explanation of the former less perfect stages of development.

As the fundamental principle for the development of the European tonal system, we shall assume that the whole mass of tones and the connection of harmonies must stand in a close and always distinctly perceptible relationship to some arbitrarily selected tonic, and that the mass of tone which forms the whole composition, must be developed from this tonic, and must finally return to it. The ancient world developed this principle in homophonic music, the modern world in harmonic music. But it is evident that this is merely an esthetical principle, not a natural law.

The correctness of this principle cannot be established à priori. It must be tested by its results. The origin of such esthetical principles should not be ascribed to a natural necessity. They are the inventions of genius, as we previously endeavoured to illustrate by a reference to the principles of architectural style.

[1]Thus in R. G. Kiesewetter’s historico-musical writings, which are otherwise so rich in facts industriously collected, there is evidently an exaggerated zeal to deny everything which will not fit into the modern major and minor modes.
[2][See App. XX. sect. K. for some of these scales. — Translator.]
[3]['Why is a consonant union of voices pleasanter than a single voice? Is the singing of voice against voice, a consonant union of voices in Octaves? This singing of voice against voice occurs when young boys and men sing together, and their tones differ as the highest from the lowest of the scale.'] Towards the end of the songs the instrumental accompaniment seems to have separated itself from the voice. Probably this is what is meant by the krousis in the passage, ['But when they end in the same, the matter is precisely similar to what occurs when they play an accompaniment to a song. For the accompanyists do not follow the rest, but when the singers return to the same, they please more in the end, than they displease in the differences before the end, by which means the common part in what is generally different, pleases more than anything but the Octave.'] See also Plutarch, De Musica, xix.xxviii. That the Greeks knew the effect of consonances and did not like it, appears by the following passage from Aristotle, De Audibilibus, ed. Bekker, p. 801: 'For this reason we understand a single speaker better than many who are saying the same things at the same time. And so with strings. And much less, when flute and lyre are played at the same time, because the voices are confused by the others. And this is very plain for the consonances. For both tones are concealed, one by the other.
[4][In Java long pieces of music in non-harmonic scales occur to accompany actions and develop the feeling of a plot. Many instruments play together, but there is no harmony. — Translator.]
[5]The αὐλοί were perhaps more like our oboes.
[6]Arist. Prob. xix. 15. 'Why are themes (nomoi) not used in antistrophic singing, while all other choral singing is employed? Is it because themes belong to public performers who are already able to imitate and extend, and hence would make their song long and very figurate? For melodies, like words, follow imitation and change. It is more necessary for melody to imitate, than for words. Wherefore dithyrambic poets also when they became mimetic, disused their previous antistrophic singing. The reason is that formerly gentlemen (eleutheroi) used to sing the choruses themselves. It was difficult for many to sing like public performers. So they rather intoned suitable melodies. For it is easier for one to make numerous variations than for many to do so, and for a public performer than for those who retained old usage. Hence the melodies were made simpler for them. Now antistrophic singing is simple, for it depends on number, and is measured by a unit. The same reason shews why the parts of the actors are not antistrophic, but those of the chorus are so. For the actor is a public performer [and a mime], but the chorus does not imitate so well.’ — Translator.]
[7][Prof. Helmholtz's observations on speaking must be read in reference to North German habits only. — Translator.]
[8]By no means uniformly, even in North Germany. The habits of different nations here vary greatly. In Norway and in Sweden the voice is regularly raised on unemphatic syllables. In Scotland the emphasis is often marked by lowering the pitch. — Translator.]
[9][These are the dates of his reign. Hullah says the school was founded in A.D. 350. — Translator.]
[10]Antony, 'Lehrbuch des Gregorianischen Kirchengesanges' [Manual of Gregorian Church-music], Münster, 1829. According to the information collected by Fétis (in his Histoire générale de Musique, Paris, 1869, vol. i. chap, vi.), it has become doubtful whether this system of declamation with prescribed cadences, is not rather to be deduced from the Jewish ritual chants. In the oldest manuscripts of the Old Testament, there are 25 different signs employed to denote cadences and melodic phrases of this kind. The fact that the corresponding signs of the Greek Church are Egyptian demotic characters, hints at a still older Egyptian origin for this notation.
[11][We must remember that the Greek and Latin so-called accents consisted solely in alterations of pitch, and hence to a certain extent determined a melody. See Dionysius of Halicarnassus,περί συνθέσεως όνομάτων, chap, xi., where we also find that in his day (first century before Christ) the musical composers transgressed at pleasure the rules of both accent and quantity. But if the written accents in Greek, and the accents as determined by the rules of grammarians in Latin, are carefully examined, it will be found that every line in a Greek or Latin poem had its own distinct melody, the art of the poet being shewn by the great variability of pitch conjoined with a constant quantity of rhythm. — Translator.]
[12]Fétis, Biographie universelle des Musiciens, vol. i. p. 126.
[13][The forefinger is ὁ λιϰανός, the note played by it is ἡ λίϰανος, accent and gender both differing. — Translator.]
[14]Arist. Prob. xix. 20. This passage has also been partly quoted by Ambrosch. [The names of Greek tones were those of the strings on the lyre by which they were played, just as if in English we were to call the tones $$g, d', a', e''$$, the tones of the fourth, third, second, and first strings respectively, because they are produced as the open notes of these strings on the violin, and contracted them to fourth, third, &c., only omitting the word string. As the violin when held sideways in playing, throws the $$g$$ string uppermost, and the $$e''$$ string the lowermost, we might in the same way call g the 'uppermost note,' ύπάτη, although lowest in pitch, and $$e''$$ the 'lowermost note,' νήτη, although highest in pitch. Then $$d$$ might be called the middle, μέση, being really the key-note of the violin and one of the two middle strings. This illustrates the Greek names very closely, for the lyre was held with the string sounding the lowest note, uppermost. See the scale on the next page. — Translator. ]
[15]Διὰ τί͵ ἐὰν μὲν η μέσῆ κινηθῆ, καὶ αἱ ἄλλαι ϰορδαὶ ἠχοῦσι ϕθεγγόμεναι (one of my colleagues, Prof. Stark, conjectures that in place of ϕθεγγόμεναι, which makes nonsense, we should read ϕθειρόμεναι) ἐὰν δὲ αὖ ἡ μὲν υένη, τῶν δ' ἄλλων τὶϛ κινηθῆ, κινηθεῖσα μόνη ϕθέγγεται; (for which Prof. Stark again proposes ϕθείρεται;) Ἢ ὅτι τὸ ἡρμόσθαι ἐστὶν ἀπάσαιϛ, [τὸ δὲ ἔχειν πωϛ πρὸϛ τὴν μέσην ἁπάσαιϛ], καὶ ἡ τάζιϛ ἡ ἑκάστηϛ, ἤδη δι' ἐκείνην; ἀρθέντοϛ οὖν τοῦ αἰτίον τοῦ ἡρμόσθαι καὶ τοῦ συνέχοντοϛ, οὐκ ἒτι ὁμοίωϛ ϕαίνεται ὑπάρχειν. Arist. Prob. xix. 36.
[16]Nicomachus, Harmonicē, lib. i. p. 6, ed. Meibomii. [The following is Nicomachus’s arrangement of the comparison, with his reasons :
Saturn hypatē, as being highest in position, ὓπατον γὰρ τὸ ἀνώτατον.
Jupiter parhypatē, as next highest to Saturn.
Mars lichanos or hypermesē, as between Jupiter and the Sun.
The Sun mesē, as lying in the middle, the fourth from either end, middlemost string and planet.
Mercury paramasē, as lying between the Sun and Venus.
Venus paraneatē, as lying just above the moon.
The moon neatē, as being lowest of all in position and next the earth, καὶ γὰρ νέατον, τὸ κατώτατον. — Translator.]
[17]Διὰ τί εὐαρμοστότερον ἀπὸ τοῦ ὀξέοϛ ἐπὶ τὸ βαρὺ, ἢ ἀπὸ τοῦ βαρέοϛ ἐπὶ τὸ ὀξύ; Πότερον ὁτι τὸ ἀπὸ τῆϛ ἆρχῆϛ γίνεται; ἡ γὰρ μέση καὶ ἡγεμὼν ὀξυτάτη τοῦ τετραχόρδου. Τὸ δὲ οὐκ ἀπ' ἀρχῆϛ, ἀλλ' ἀπὸ τελευτῆϛ. Ἤ ὄτι τὸ ϐατὺ ἀπὸ τοῦ ὀξέοϛ γενναιότερον, καὶ εὐϕωνότερον; Arist. Prob. xix. 33.
[18]Διὰ τί δὲ ταύτην [τὴν παρυπάτην] χαλεπῶϛ [ἄδουσι], τὴν δὲ ὑπάτην ῥᾳδίωϛ· καίτοι δίεσιϛ έκατέραϛ; ᾒ ὄτι μετ' ἀνέσεωϛ ἡ ὑπάτη, καὶ ἃμα μετὰ τὴν σύστασιν ἐλαϕρὸν τὸ ἄνω βάλλειν; Arist. Prob. xix. 4.
[19][This would be entirely crossed by the ancient Greek system of pitch-accents, just as it now is by a similar system in Norwegian, where the pitch may rise for both affirmative and interrogative sentences. See footnote 12.— Translator.]
[20]Among the presumed ancient melodies which have been handed down to us, the fragment of the Homeric Ode to Dēmētēr, which has been published by B. Marcello, shews the above-mentioned peculiarity very distinctly.
[21][Mr. Rockstro in his article 'Ambrosian Chant,' in Grove's Dictionary of Music, states that this attribution of four authentic scales to St. Ambrose has not been proved. — Translator.]
[22]Jones, On the Music of the Indians, translated by Dalberg, pp. 36, 37. [Sir W. Jones's tract, with many others, is reprinted in Sourindro Mohun Tagore's Hindu Music from Various Authors. This is what he says of the ans'a, p. 149 of Tagore: 'Since it appears from the Náráyan [a Sanscrit treatise on music], that 36 modes are in general use, and the rest very rarely applied to practice, I shall exhibit only the scales of the 6 Rágas [tunes] and 30 Ráginis [female personification of tunes in Hindu music] according to Sóma. ...Three distinguished sounds in each mode [as Sir W. Jones translates rág] are called graha, nyása, ans'a, and the writer of the Náráyan defines them in the two following couplets. [I give the translation only.] "The note called graha is placed at the beginning, and that named nyása at the end of a song; that note, which displays the peculiar melody, and to which all the others are subordinate, that, which is always of the greatest use, is like a sovereign, though a mere ans'a or portion." "By the word vádi," says the commentator, "he means the note, which announces and ascertains the Rága [tune], and which may be considered as the parent and origin of the graha and nyásá." This clearly shews, I think [says Sir W. Jones], that the ans'a must be the tonic; and we shall find that the two other notes are generally its third and fifth, or the mediant and dominant. In the poem entitled Māgha there is a musical simile, which may illustrate and confirm our idea. [I give the translation only.] "From the greatness, from the transcendent qualities of that hero, eager for conquest, other kings match in subordination to him, as other notes are subordinate to the ans'a." — Translator.]
[23][The construction and time are very different. The scales are extremely variable. The results are very imperfectly represented by our present musical notation. — Translator.]
[24]Histoire de l'Harmonie au moyen Age, Paris, 1852, pp. 5-7.
[25]Geschichte des Claviers [History of the Pianoforte], Leipzig, 1868, p. 49.
[26]Coussemaker, loc. cit. Discant: Custodi nos, Pl. xxvii. No. iv., translated in p. xxvii. No. xxix.
[27]Winterfeld, Johannes Gabrieli und sein Zeitalter, vol. ii. p. 41.
[28]Winterfeld, ibid., vol. ii. p. 19 and p. 59.
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